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Revealed preference and indifferent selection

Abstract : It is shown that preferences can be constructed from observed choice behavior in a way that is robust to indifferent selection (i.e., the agent is indifferent between two alternatives but, nevertheless, is only observed selecting one of them). More precisely, a suggestion by Savage [Savage, L.J., 1954. The foundations of statistics. John Wiley and Sons] to reveal indifferent selection by considering small monetary perturbations of alternatives is formalized and generalized to a purely topological framework: preferences over an arbitrary topological space can be uniquely derived from observed behavior under the assumptions that they are continuous and nonsatiated and that a strictly preferred alternative is always chosen, and indifferent selection is then characterized by discontinuity in choice behavior. Two particular cases are then analyzed: monotonic preferences over a partially ordered set, and preferences representable by a continuous pseudo-utility function.
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Eric Danan. Revealed preference and indifferent selection. Mathematical Social Sciences, Elsevier, 2008, 55, pp.24-37. ⟨10.1016/j.mathsocsci.2006.12.005⟩. ⟨hal-00872255⟩

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